A Novel Parameter-Dependent Inverse Gaussian Distribution Considering Random Effects with Extension to Accelerated Life Test

Inverse Gaussian distribution is one of the most important distributions in reliability evaluation. The relevance between parameters is neglected in traditional distribution modeling, which weakens the precision of reliability analysis. In this paper, a parameter-dependent inverse Gaussian distribution considering random effects is proposed based on the failure mechanism equivalence. We consider that the scale parameter of the inverse Gaussian distribution is linearly related with the shape parameter, while the scale parameter is regarded as a random variable. Further, the proposed distribution model is extended to accelerated life test for improving the applicability of inverse Gaussian distribution in reliability engineering. EM algorithm is adopted for parameter estimation. The validity and stability of the parameter estimation method are verified by simulation studies.